Dalziel J. Wilson

Measurement-based control of a mechanical oscillator at its thermal decoherence rate

In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen successful applications of these protocols in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. However, stabilizing the quantum state of a tangibly massive object, such as a mechanical oscillator, remains very challenging: the main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, 4.3-megahertz nanomechanical oscillator in the timescale of its thermal decoherence, a basic requirement for real-time (Markovian) quantum feedback control tasks, such as ground-state preparation. The sensor is based on evanescent optomechanical coupling to a high-Q microcavity, and achieves an imprecision four orders of magnitude below that at the standard quantum limit for a weak continuous position measurement—a 100-fold improvement over previous reports—while maintaining an imprecision–back-action product that is within a factor of five of the Heisenberg uncertainty limit. As a demonstration of its utility, we use the measurement as an error signal with which to feedback cool the oscillator. Using radiation pressure as an actuator, the oscillator is cold damped with high efficiency: from a cryogenic-bath temperature of 4.4 kelvin to an effective value of 1.1 ± 0.1 millikelvin, corresponding to a mean phonon number of 5.3 ± 0.6 (that is, a ground-state probability of 16 per cent). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of mechanical oscillators as practical subjects for measurement-based quantum control.

Enhancement of mechanical Q factors by optical trapping.

The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and for observing quantum behavior. Here, we demonstrate a technique to push the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen or trap a particular motional mode. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly lossless optical potential, thereby strongly diluting the effect of material dissipation. By placing a 130 nm thick SiO2 pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q=5.8(1.1)×10(5), representing more than an order of magnitude improvement over the conventional limits of SiO2 for this geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems.

Appearance and Disappearance of Quantum Correlations in Measurement-Based Feedback Control of a Mechanical Oscillator

Quantum correlations between imprecision and backaction are a hallmark of continuous linear measurements. Here, we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nanomechanical oscillator. Backaction imparted by the meter laser, due to radiation-pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e., feedback that suppresses measurement backaction, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to backaction arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits, of measurement-based feedback as a tool to manipulate quantum correlations.

Quantum Correlations of Light from a Room-Temperature Mechanical Oscillator

We observe quantum correlations imprinted on an optical beam interacting with a room temperature nanomechanical oscillator, and show how this leads to an enhancement in the relative signal-to-noise ratio for the estimation of an arbitrary force.

Suppression of extraneous thermal noise in cavity optomechanics.

Extraneous thermal motion can limit displacement sensitivity and radiation pressure effects, such as optical cooling, in a cavity-optomechanical system. Here we present an active noise suppression scheme and its experimental implementation.

A strongly coupled Λ-type micromechanical system

We study a classical Λ-type three-level system based on three high-Q micromechanical beam resonators embedded in a gradient electric field. By modulating the strength of the field at the difference frequency between adjacent beam modes, we realize strong dynamic two-mode coupling, via the dielectric force. Driving adjacent pairs simultaneously, we observe the formation of a purely mechanical “dark” state and an all-phononic analog of coherent population trapping—signatures of strong three-mode coupling. The Λ-type micromechanical system is a natural extension of previously demonstrated “two-level” micromechanical systems and adds to the toolbox for engineering of all-phononic micromechanical circuits and arrays.

Elastic strain engineering for ultralow mechanical dissipation

Better performance under stress Engineering stress or strain into materials can improve their performance. Adding mechanical stress to silicon chips, for instance, produces transistors with enhanced electron mobility. Ghadimi et al. explore the possibility of enhancing the vibrational properties of a micromechanical oscillator by engineering stress within the structure (see the Perspective by Eichler). By careful design of the micromechanical oscillator, and by building in associated stresses, exceptional vibrational properties can be produced. Such enhanced oscillators could be used as exquisite force sensors. Science, this issue p. 764; see also p. 706 Engineered stress is used to fabricate micromechanical oscillators with enhanced vibrational properties. Extreme stresses can be produced in nanoscale structures; this feature has been used to realize enhanced materials properties, such as the high mobility of silicon in modern transistors. We show how nanoscale stress can be used to realize exceptionally low mechanical dissipation when combined with “soft-clamping”—a form of phononic engineering. Specifically, using a nonuniform phononic crystal pattern, we colocalize the strain and flexural motion of a free-standing silicon nitride nanobeam. Ringdown measurements at room temperature reveal string-like vibrational modes with quality (Q) factors as high as 800 million and Q × frequency exceeding 1015 hertz. These results illustrate a promising route for engineering ultracoherent nanomechanical devices.

Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics

Abstract We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a 1 / f thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, ϕ = 4.5 ⋅ 10 − 6 , agrees well with the quality factor (Q) of the fundamental beam mode ( ϕ = Q − 1 ). In conjunction with Q measurements made on higher order flexural modes, and accounting for the mode dependence of stress-induced loss dilution, we find that the intrinsic (undiluted) loss angle of the beam changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the impact of such “structural damping” on experiments in quantum optomechanics, in which the thermal force acting on a mechanical oscillator coupled to an optical cavity is overwhelmed by radiation pressure shot noise. As an illustration, we show that structural damping reduces the bandwidth of ponderomotive squeezing.

Gallium phosphide microresonator frequency combs (Conference Presentation)

Gallium phosphide (GaP) is an attractive material for non-linear optics because of its broad transparency window (λ_vac > 548 nm) and large Kerr coefficient (n_2 ~ 6 × 10^-18 m^2/W). Though well-established in the semiconductor industry as a substrate for visible LEDs, its use in integrated photonics remains limited due to fabrication challenges. Recently we have developed a method to integrate high quality, epitaxially-grown GaP onto silica (SiO2) based on direct wafer bonding to an oxidized silicon carrier wafer. Here we exploit this platform to realize unprecedentedly low loss (Q > 3 × 10^5) GaP-on-SiO2 waveguide resonators which have been dispersion-engineered to support Kerr frequency comb generation in the C-band. Single-mode, grating-coupled ring resonators with radii from 10 – 100 μm are investigated. The threshold for parametric conversion is observed at input powers as little as 10 mW, followed by 0.1 – 1 THz frequency comb generation over a range exceeding 400 nm, in addition to strong second- and third-harmonic generation. Building on this advance, we discuss the prospects for low-noise, sub-mW-threshold soliton frequency combs with center frequencies tunable from the mid-IR to the near-IR. Applications of such devices range from precision molecular spectroscopy to ultrafast pulse generation to massively parallel coherent optical communication.

Cavity Optomechanics: Controlling Mechanical Motion with Radiation Pressure

Here we review recent progress on quantum coherent coupling, optomechanically induced transparency as well as switching, slowing and advancing of pulses via nano-optomechanical systems. Moreover the interaction of nanomechanics with two-level-defect states is discussed.